1. The following function represents the cots in hundreds of dollars for producing pens, where x represents 1000's of units
c(x)=.4x^2-16x+200 , 25 ≤ x ≤ 40

a) Estimate the cost for making the 36th 1000-unit run using the marginal cost function derivative.

b) Find the actual cost for making the 36th 1000-unit run.

c) Find the percent margin of error for your cost estimate in part a.

2. Originally Posted by Hallah_az
2. Find the equation of the line tangent to f(x)=1/x at the point x=1
You need to find the derivative.
Thus, you have $\displaystyle f(x)=\frac{1}{x}=x^{-1}$
Its derivative is the power rule, thus,
$\displaystyle f'(x)=(-1)x^{-1-1}=-x^{-2}=-\frac{1}{x^2}$
At, point $\displaystyle x=1$ we have, $\displaystyle y=\frac{1}{1}=1$.
Now we use the point-intercept formula. Which says that if a line passes through point $\displaystyle (x_0,y_0)$ and has slope $\displaystyle m$ then, its equation is,
$\displaystyle y-y_0=m(x-x_0)$. Thus, in this case we have the point, which is $\displaystyle (1,1)$. Now we need the slope. That is the derivative evaluated at that point which is $\displaystyle f'(1)=-\frac{1}{1^2}=-1$ the equation is,
$\displaystyle y-1=-1(x-1)$
Thus,
$\displaystyle y-1=-x+1$
Thus,
$\displaystyle y=-x+2$

3. ## Thank you!

I got the 2nd part, but I do not understand a) the marginal cost function; b) actual cost; c) the percent margin

Could you please explain. Thank you for all your help!